Fractal analysis of the inhomogeneous spatial structures of the boundary lubricating layer in the friction processes

The synergetic model, that allows representing the processes proceeding at the boundary friction of two atomically smooth surfaces divided by an ultrathin layer of lubricant material is studied. The model is based on the Lorenz system, which is parameterized by shear stresses, shear strain and lubricant film temperature. The spatial inhomogeneity has been considered and it has been shown that a domain structure with two types of domains is formed during the friction process of contact surfaces planes through lubricant. The time dependencies of fractal dimensions of the domain distributions on a plane have been calculated and it has been shown that there is a time point, when fractal dimensions take the minimum values. It has been found, that the system tends to the homogeneous state, in which the same value of the shear stresses specifying the relative rate of the rubbing surfaces, is realized all over the contact plane.